4.2.1 Retrieval Characteristics
Atmospheric retrievals from MCS observations provide vertical profiles of pressure, p, (Pa), temperature, T, (K), dust opacity, i.e., fractional extinction due to dust per unit height, dzτ, (km-1) at 463 cm-1, and water ice opacity (km-1) at 842 cm-1. All of the
vertical profile quantities except pressure are gridded on pressure coordinates at
approximately a factor of five higher resolution than the ~5 km vertical resolution of the instrument detector array (and thus the retrievals). The pressure at the surface, ps, (Pa) is extrapolated from the pressure retrieval using the hydrostatic equation. Kleinböhl et al.
[2009] provides both a history of data and retrieval coverage and also a description of the retrieval algorithm and an evaluation of its success under different observational
retrievals analyzed here use an advanced version of the retrieval algorithm, which includes a simple scattering approximation in the radiative transfer.
Retrievals from limb observations have an important limitation key to these investigations. The lowest detector used for the retrieval of dust must have a line-of-sight (LOS) opacity less than 2.5 and a contribution of less than 10% from the surface in the detector field of view (FOV). (Note that the airmass factor in the limb is ~50.) The practical effect is that retrieved vertical profiles of dust (with rare exceptions) do not include information from detectors observing limb paths less than ~8 km above the surface. Thus, they provide limited information about dust within the lowest scale height of the atmosphere. In some cases, retrieved profiles only use information from detectors observing at higher levels than ~8 km above the surface, further limiting information about low-level dust.
A small number of retrievals from late northern summer of MY 28 are generally omitted from this analysis. Between 9 February 2007 and 14 June 2007 (Ls=180°—257° of MY 28), MCS operated in a mode known as “limb staring” in which the limb was observed at a constant angle relative to the spacecraft. This degraded mode of operation primarily affects the altitude range of the atmosphere observed by the instrument and the calibration of the data. Therefore, retrievals from data collected from this period provide less information about high altitudes in the southern hemisphere and low altitudes near the north pole than retrievals from data collected when the instrument was scanning the limb. In addition, retrievals from limb staring data have greater uncertainties in areas of the atmosphere where radiances are low due to the poor calibration of the instrument in
scanning retrievals (in which the limb is observed at varying angles) are good [Kleinböhl
et al., 2009], but the limited vertical range of limb staring retrievals (and hemispheric
differences in the vertical range) makes reconstruction of the dust distribution more difficult.
4.2.2 Zonal Averaging and Derived Quantities
To avoid biasing of zonal averages by heavier sampling at particular longitudes, the retrievals are separated into “dayside” (9:00—21:00 LST) and “nightside” (21:00—9:00 LST) bins and further binned in 36 (5° resolution) mean latitudinal bins, 64 (5.625° resolution) mean longitudinal bins, and Ls bins at 5° resolution: a resolution comparable to Mars general circulation model grids. Mean latitude and longitude refer to the
coordinates at the tangent point observed by the center of the MCS detector array at ~40 km above the surface. Since MCS retrievals have relatively broad horizontal weighting functions biased in the direction of the detector array, this latitude and longitude is usually a better indicator of the location of even dust retrieved near the surface than the latitude and longitude at which the limb intersects the surface.
Caution must be exercised when averaging aerosol opacity retrievals. Aerosol opacity is not reported at all in some retrievals for a variety of reasons, such as that there is a high likelihood of misattribution of opacity to one aerosol vs. another, as happens with carbon dioxide ice and dust at the winter pole. See Kleinböhl et al. [2009]for further discussion. Retrievals without any reported aerosol opacity are not included in the
Pa. At pressures higher than 200 Pa, there is not enough information to retrieve aerosol opacity accurately. At pressures lower than 20 Pa, the radiance contributed by the aerosol opacity is comparable to the noise of the radiance measurements. In the averaging
process, the unreported aerosol opacity at high pressures is not included, that is, the average of the retrieved aerosol opacity at 200 Pa is the average of all aerosol opacities reported at 200 Pa. But since the unreported opacity on the lower pressure end is unreported because it is so low, the retrieval is altered so that these unreported values have a value of 0 instead. This averaging routine minimizes the effects of a small number of retrievals with measurable aerosol opacity at high altitudes.
The variability in the longitudinal sampling of the zonal averages is depicted in Figures 4.1a and 4.1b. Longitudinal sampling is controlled by a variety of factors, some of which are intrinsic to the data as collected by the instrument, e.g., periods in which data was not collected because the instrument was stowed, and some of which are related to the limitations of the retrieval algorithm, e.g., the exclusion of retrievals with a bad pressure retrieval due to high LOS optical depth in the channels used for pressure
retrieval. The absolute breaks in coverage in an Ls bin are indicated in white. The break at Ls=210° during MY 28 is a period during which the instrument was stowed.
Figures 4.1a and 4.1b suggest longitudinal sampling by dayside profiles is much poorer than from nightside profiles. In fact, dayside coverage over the equator is
practically non-existent. This discrepancy is not well understood but may be due to incorrect representation in the retrieval algorithm of the scattering by tropical water ice clouds of upwelling radiation from the surface.
Figure 4.1. (a) Percentage of longitudes in the binning scheme described in Chapter 4.2.2 sampled by nightside retrievals vs. latitude and Ls; (b) percentage of longitudes in the binning scheme described in
Chapter 4.2.2 sampled by dayside retrievals as a function of latitude and Ls; (c) 100*R2 for the empirical
fitting scheme described in Chapter 4.3.2 for nightside retrievals as a function of latitude and Ls;
(d) 100*R2 for the empirical fitting scheme described in Chapter 4.3.2 for dayside retrievals as a function of latitude and Ls.
4.2.3 A5 Channel Opacity and the Utility of Density
Scaled Opacity
For a variety of scientific and engineering applications (including some discussed in this Chapter), opacity in the A5 channel is not a particularly convenient or intuitive quantity to use. However, it is the retrieved quantity related to dust that most immediately follows from MCS observations of radiance. The conversion factor between A5 channel opacity and visible opacity at 600—700 nm is ~7.3. This factor differs from what is reported in
Kleinböhl et al. [2009], because it accounts for the higher visible/infrared opacity ratio of
the smaller dust particles assumed in the new retrieval algorithm [Clancy et al., 2003]. Given some model of the size, shape, and composition of the dust particles, opacity can be converted to three other quantities: volumetric number density, Nv; mass number density, Nm; and mass mixing ratio, q. For consistency’s sake, I make the same assumption as used in the retrieval algorithm: that the dust is compositionally uniform and made of spherically symmetric particles with a modified gamma size distribution of the form:
€
n(r)∝raexp(
−brc) (4.1)
The parameters used for the dust distribution in the version of the retrieval dataset used here are not the same as in Kleinböhlet al. [2009] but have been tuned to minimize misfitting error in the retrieval algorithm.
Following Taylor et al. [2007], the opacity as a function of the volumetric number density is: € dzτ= Qextπr2Nvn(r)dr 0 ∞
∫
(4.2)a function of the dust distribution, not of radius, such that: € Nv = dzτ Qextπ r 2 n(r)dr 0 ∞
∫
(4.3)The value of Qext used by the retrieval algorithm is 0.35.
€
π r2n(r)dr 0
∞
∫
in Eq. 4.3 is the average geometric cross-section of the distribution, G. So Eq. 4.3 becomes:€
Nv = dzτ
QextG (4.4)
where G is assumed to be 1.26 (µm)2 in the retrieval algorithm. So Nv (m-3)=2.3×109dzτ (km-1). The mass number density, Nm, then can be obtained by dividing Nv by the atmospheric density, ρ.
The mass mixing ratio is obtained similarly. Scaling Eq. 4.3 by ρ, we obtain the density-scaled opacity: € dzτ ρ = NvQextπ ρ r 2n(r)dr 0 ∞
∫
(4.5)We can form an expression for the mass mixing ratio by calculating the ratio between the mass of dust particles in a given volume and the mass of air in the same volume:
€ q= ρDNv 4 3πr 3 n(r)dr 0 ∞
∫
ρ (4.6)€ q= 4 3 ρD Qext dzτ ρ r3 n(r)dr 0
∫
r2n(r)dr 0 ∞∫
(4.7)The integral ratio above is equal to “the effective radius,” reff, which is 1.06 µm for the distribution used by the retrieval algorithm. So:
€ q= 4 3 ρD Qext dzτ ρ reff (4.8) Assuming ρD=3000 kg m-3, q (ppm) =1.2×104dzτ/ρ (m2 kg-1).
Since these derivations are model dependent, we only will report dzτ and dzτ/ρ, which can be derived from the retrievals directly. For dust with definite, spatially and temporally invariant distributions of size, shape, and composition, the number density is linearly proportional to dzτ, and the mass mixing ratio is linearly proportional to dzτ/ρ.
If Eq. 4.8 is re-arranged, dzτ/ρ is proportional to the product of Qext/reffand q. The parameter Qext is dependent on the size distribution, so that if there is significant particle size segregation in the atmosphere, variability with size in Qext/reff could result in
inferring an apparent enhancement of mass mixing ratio above the surface when no enhancement is actually present. For example, if small dust particles lie over large ones and Qext/reff is significantly larger for small particles, a given mass mixing ratio of small particles will have greater opacity than the same mass mixing ratio of large particles. Table 4.1 shows the results of Mie scattering simulations of Qext for dust size
distributions with different reff but the same variance as the size distribution used in the retrievals. The variability in the ratio over a reasonable size range for dust is no more
channel to particle size
reff (µm) Qext/reff (µm-1) Qext/reff normalized by the
value at 1.06 µm 0.75001 0.3095 0.970 1.06070 0.3305 1 1.50000 0.3619 1.10 2.12160 0.3956 1.20 2.99930 0.4137 1.25 4.2432 0.3998 1.21 5.99960 0.3524 1.07
micron-sized particles will produce an apparent depletion of mass mixing ratio in a truly uniformly mixed profile. This analysis, however, does not consider the effect on the retrieval procedure of assuming different particle size distributions.
The rough interchangeability of mass mixing ratio and density scaled opacity is useful for understanding the radiative and dynamical significance of particular vertical profiles of dust. In an optically thin atmosphere (even for non-uniform dust), the quantity
dzτ/ρ also is proportional to the unit heating rate per unit mass due to dust at fixed wavelength, J. Thus, the dust mass mixing ratio (outside of dust storm conditions) is a good proxy for the diabatic heating rate and vice versa.